Improvements of Higgs mass predictions in supersymmetric theories

Transcription

1 Improvemens of Higgs mass predicions in supersymmeric heories Heidi Rzehak Alber-Ludwigs-Universiä Freiburg in coll. wih T. Hahn, S. Heinemeyer, W. Hollik and G. Weiglein FeynHiggs collaboraion Dec. 13, 2013

2 Calculaion of Higgs masses in he MSSM Two approaches: Feynman diagrammaic approach (or effecive poenial approach for vanishing exernal momena) renormalizaion group equaion approach

3 Feynman diagrammaic approach Calculae Feynman diagrams which conribue o he Higgs-boson self energies ˆΣ: h h i h + g + h h j i j h loop level O(α ) 2-loop level O(α α s ) Counererm conr. α (op Yukawa coupl.) 2

4 Feynman diagrammaic approach Two-poin-funcion: iˆγ(p 2 ) = p 2 M(p 2 ) wih he marix: h ( M 2 M(p 2 hborn )= ˆΣ hh (p 2 ) ˆΣ Hh (p 2 ) ) ˆΣ Hh (p 2 ) M 2 H Born ˆΣ HH (p 2 ) h (CP-conserving case: mixing only beween CP-even Higgs bosons h, H)

5 Feynman diagrammaic approach Calculae he zeros of he deerminan of ˆΓ: de[p 2 M(p 2 )] = 0 or calculae he eigenvalues λ(p 2 ) of M(p 2 ) (FeynHiggs approach): de[λ(p 2 ) M(p 2 )] = 0 and solve ieraively: p 2 λ(p 2 ) = 0 loop-correced Higgs mass values

6 Renormalizaion group equaion approach Assumpion: all SUSY paricles and he CP-odd Higgs boson mass M A being heavy M S (i) Mach quaric Higgs coupling λ a scale M S (ii) Use SM-RGE running o obain λ a scale m (iii) Higgs mass is given by mh 2(m ) = 2λ(m )v 2 wih v 174 GeV being he Higgs vacuum expecaion value Approach can be refined o allow for differen scales

7 Advanages Feynman diagrammaic approach: All log- and non-log erms are aken ino accoun a a cerain order of perurbaion heory: Especially imporan for lower mass scales Renormalizaion group equaion approach: Resummaion of poenially large log-erms: Especially imporan for larger mass scales Combine boh approaches

8 Combinaion Feynman diagrammaic par: from FeynHiggs Renormalizaion group equaion (RGE) par: 2-loop RGE for running [Espinosa, Quiros 91] µ dλ(µ) dµ = 1 [12λ ] 2 (16π y 2 4 λ 12y ) 1 [ ] + (16π 2 ) 2 78λ y 6 3λy 4 64g 2 s y λg 2 s y 2 72λ 2 2 y µ dg s(µ) dµ µ dy (µ) dµ = g [ ] s 2 (16π 2 7g s + g [ ] s ) (16π 2 ) 2 26g 4 s 2g 2 2 s y = y [ ] 9 (16π 2 ) 2 y 2 2 8g s y + (16π 2 ) 2 quaric Higgs coupling srong coupling op Yukawa coupling [ 12y λ2 6λy g 2 s y g s ]

9 Combinaion Renormalizaion group equaion (RGE) par: (coninued) Maching a scale M S = m 1 m 2 : [Carena, Haber, Heinemeyer, Hollik, Wagner, Weiglein, hep-ph/ ] [ ] λ(m S ) = 3y 4 X 2 8π 2 M 2 1 X 2 S M 2 S m i = sop masses X = A µ co β = squark mixing parameer leading + nex-leading log (ln M S m ) resummaion

10 Combinaion Combinaion of boh approaches: Avoid double couning of logs Subrac logs from he Feynman diagrammaic (FD) resul: M 2 h = ( M2 h )FD (X OS ) ( Mh 2)FD,log (X OS ) + ( Mh 2)RGE (X MS Boh approaches use a MS op quark mass FD: X in on-shell scheme, RGE: X in MS scheme: Conversion needed: X MS = X OS [ 1 + ln M2 S m 2 ( αs π 3α ) ] 16π )

11 Combinaion For M A M Z : ˆΣ φuφ u (sin β) 2 M 2 h self energy of he ineracion eigensaes φ u φ u couples o up-ype quarks Correcion can be incorporaed ino he self energy marix

12 M h [GeV] Resuls Higgs mass dependence on X /M S and M S : preliminary FeynHiggs M S = 1 TeV M S = 2 TeV M S = 5 TeV M S = 10 TeV M S = 15 TeV M S = 20 TeV lower scales: maxima: large difference in size due o non-log erms larger scales: differences beween maxima become smaller (sill sizeable in beween) X /M S [GeV] M A = M 2 = µ = 1 TeV, m g = 1.6 TeV, an β = 10

13 M h [GeV] Resuls FH295 3-loop 4-loop 5-loop 6-loop 7-loop LL+NLL preliminary FeynHiggs X /M S = 2 X = M S [GeV] M A = M 2 = µ = 1 TeV, m g = 1.6 TeV, an β = 10 Comparison of: old FeynHiggs reliable up o M s = O(1TeV) analy. soluion of RGE: 3-loop... 7-loop level numerical soluion: logs resummed o all orders

14 M h [GeV] Resuls loop, O(α α s 2 ) 3-loop full LL+NLL H3m preliminary FeynHiggs A 0 = 0, anβ = M S [GeV] Comparison wih H3m: [Kan, Harlander, Mihaila, Seinhauser, arxiv: ] 3-loop: O(α α 2 s), O(α 2 α s), O(α 3 ), only leading and nex-o leading logs single scale M S H3m: complee O(α α 2 s) resul differen scales A 2-loop: differen ren. schemes CMSSM: m 0 = m 1/2 = GeV, A 0 = 0, an β = 10, µ > 0, specra generaion wih SofSUSY [Allanach, hep-ph/ ]

15 Conclusion Lower SUSY scales: Feynman diagrammaic approach (or effecive poenial approach) Large SUSY scales: Renormalizaion group equaion approach Consisen combinaion of boh approaches: Good predicion for all scales Furher refinemens: Allow for: smaller CP-odd Higgs boson masses large sop mass spliing